I am trying to show that the eigenvalues of a matrix are described by my proposed formula. I managed to show this numerically, but I would like to show this symbolically. There are two issues here - the orders of the two lists are different, and the forms are different (sums of complex exponentials vs RootOfs). Any suggestions?

>  restart; >  with(LinearAlgebra): with(GraphTheory): with(plots): >  L:=9; Generate a matrix and its eigenvalues >  C := AdjacencyMatrix(CycleGraph(L, directed)): Id := IdentityMatrix(L): A := KroneckerProduct(C, Id) + KroneckerProduct(Id, C) + KroneckerProduct(C, C): evs := Eigenvalues(A, output = list): plotevs := complexplot(evs, style = point, color = blue, scaling = constrained): My guess as to their values >  evstheory:=[seq(seq(exp((2*Pi)*I*k/L) + exp((2*Pi)*I*m/L) + exp((2*Pi)*I*(m + k)/L), k = 0 .. L - 1), m = 0 .. L - 1)]: plotevstheory:=complexplot(evstheory, style = point, color = red, scaling = constrained): They look to be the same >  display(Array([plotevs,plotevstheory]));         Even showing they are the same numerically is nontrivial because the sorting is not consistent >  fnormal(sort(evalf(evs))-sort(evalf(evstheory))); This succeeds, so they are the same >  fnormal(sort(evalf[20](evs),key=evalf)-sort(evalf[20](evstheory),key=evalf)); What about symbolically? [Edit - only part of output shown] >  ans1:=simplify(sort(evs,key=evalf)-sort(evstheory,key=evalf)); >

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For a table

T := table(sparse = {}, [1 = {a}, 2 = {b}])

T[3] returns {}. 

Is there an equivalent for an rtable?

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I am trying to understand the SymmetryGroup returned in the Logic Package. The help page says "The group is a permutation group; its elements are those permutations which preserve the Boolean structure of expr." [my bold], but later the definition is given as "A symmetry of a Boolean expression expr is a mapping f of each variable to some other variable or negated variable, such that the image of expr after applying f to each of its variables is a Boolean formula which is equivalent to expr." Is logically equivalent meant here, or something else? The help page examples don't answer this question.

The following example shows that a group permutation does not lead to a logically equivalent statement as I was expecting - is this a bug, or am I expecting too much here?

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The following worksheet was run from my desktop and finds both currentdir() and interface(worksheetdir) to be "C:\Users\dharr\Desktop" (either from opening it within Maple 2017 or double-clicking on it). The startup code is

DocumentTools:-SetProperty("TextArea0",value,currentdir());
DocumentTools:-SetProperty("TextArea1",value,interface(worksheetdir));

But if I load it from Maple Player 2018, then both currentdir() and interface(worksheetdir) are "c:\program files\maple player".

It means an interactive application that runs in Maple won't run in Maple Player.

Is this a bug or deliberate strategy to make it harder to open datafiles within Maple Player?

(Can't load the worksheet contents right now)

Download Test.mw

I'm really after a simple workaround for a file open dialog with embedded components - any suggestions?

View 127_phase coloring.mw on MapleNet or Download 127_phase coloring.mw
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I am trying to color  3D plots according to phase using color=argument(x)/Pi/2

I get different results depending on the form I enter the expression x, as shown on the worksheet. Any suggestions to make this consistent?